The game's depth and complexity. Get a couple favorite dwarves and you can get a story about them, just from happenings within the game. Every dwarf (and indeed every creature but the game only shows you all the details for creatures you control) have different personalities, and different appearances. Every. single. one. And much of the game's systems come about more or less organically.
A dwarf's family all get killed in a mining accident. You don't know how they will respond to it because there are dozens of variables. They could get angry and start punching people and throwing furniture, they could go insane with sadness possibly attempting suicide, they could go berserk killing everyone in their path until killed, or they could remain calm. All dependent on how happy overall they are in the fortress, and what their personality is.
It is one of those games that really shine if you have the imagination to see the story that emerges.
And as a modder I'm also obligated to tell you about the modding aspect of the game. The game has a relatively simple(compared to other systems I've seen) tag based system for modding where a tag in a text file gives fairly good amounts of control of various behaviors. A simple group of letters like [CARNIVORE] for example gives the game all kinds of information on what a creature can and cannot eat. Most of the core gameplay is hardcoded, but you can create custom creatures, civilisations, many custom objects, custom workshops, the custom 'reactions' to preform custom jobs in those workshops, metals, stones, plants, trees, grasses, languages, worlds, engravings...the list goes on.
It's a truely awesome game... once you overcome the learning cliff. Remember that losing is fun, and many players lost many a fortress before finally learning the game well enough to make something that can last more than an ingame year.